Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 281 days μ=281 days and standard deviation sigma equals 28 days.

(b) Suppose a random sample of 21 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

The sampling distribution of x is _____ (skewed left, skewed right, normal) with u-x = _____ and o-x= _____. (Round to 4 decimal places as needed)

Answer 1

Normal distribution with,

  $\mu$ = 281

$\sigma$ = 28

A sample of size n = 21 is taken from this population.

Here , although the sample size is small , the sampling distribution of the sample mean is normal because the population distribution is normal.

The sampling distribution of the $url=https://latex.codecogs.com/gif.latex?%5Cbar%20x&t=1572555410&ymreqid=50870fb5-0ab3-84d7-1c61-ce007e01d800&sig=ObQrU3CejGhuvaPpjktQ0w--~C$ is normal with

$\mu_{\bar x}$ = $\mu$ = 281 and $\sigma_{\bar x}$ =    $\frac{\sigma}{\sqrt{n}}$ = 28/$\sqrt{}$​21 = 6.1101

Answer :

The sampling distribution of the $url=https://latex.codecogs.com/gif.latex?%5Cbar%20x&t=1572555410&ymreqid=50870fb5-0ab3-84d7-1c61-ce007e01d800&sig=ObQrU3CejGhuvaPpjktQ0w--~C$ is normal with  $\mu_{\bar x}$ =  281 and $\sigma_{\bar x}$ = 6.1101